Grade 8 Mathematics Sample ER Item Form Claim 3 MAT.08.ER.3.0000G.F.011 Claim 3 Sample Item ID: Grade: Primary Claim: Secondary Claim(s): Primary Content Domain: Secondary Content Domain(s): Assessment Target(s): MAT.08.ER.3.0000G.F.011 08 Claim 3: Communicating Reasoning Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Claim 2: Problem Solving Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Geometry 3 F: Base arguments on concrete referents such as objects, drawings, diagrams, and actions. 1 I: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Standard(s): Mathematical Practice(s): DOK: Item Type: Score Points: Difficulty: Key: Stimulus/Source: Target-specific attributes (e.g., accessibility issues): Notes: 2 A: Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace. 8.G.9 1, 5, 7 3 ER 3 M See Sample Top-Score Response. Part of PT set Version 1.0 Grade 8 Mathematics Sample ER Item Form Claim 3 Part A This sphere has a 3-inch radius. What is the volume, in cubic inches, of the sphere? Volume = cubic inches Part B This right cylinder has a radius of 3 inches and a height of 4 inches. What is the volume, in cubic inches, of the cylinder? Volume = cubic inches Version 1.0 Grade 8 Mathematics Sample ER Item Form Claim 3 [Directions to students on the computer before progressing to Part C] You will not be allowed to return to Part A or Part B of this task after submitting your answers and clicking Next. Part C Lin claims that the volume of any sphere with a radius of r inches is always equal to the volume of a cylinder with a radius of r inches and a height of h inches, when h = 4 r. 3 Show all work necessary to justify Lin’s claim. Version 1.0 Grade 8 Mathematics Sample ER Item Form Claim 3 Sample Top-Score Response: Part A: 36 cu in. (or any number between 113 and 113.1) Part B: 36 cu in. (or any number between 113 and 113.1) Part C: equal, I can create the following equation if the volume of the sphere and cylinder are 4 3 r r 2 h 3 ( 2 I can divide both sides of the equation by π r ) as shown below. 4 3 r r 2 r 2 h r 2 3 This justifies Lin’s claim. 4 rh 3 Scoring Rubric: Responses to this item will receive 0-3 points, based on the following: 3 points: The student shows a thorough understanding of the volume of spheres and cylinders. The student correctly determines the volume of both the sphere ( 36 ) and the cylinder ( 36 ) and provides a clear justification in Part C. 2 points: The student shows a partial understanding of the volume of spheres and cylinders. The student either gets both volumes correct but does not provide a clear justification for Part C OR the student gets only Part A or Part B correct AND provides a clear justification in Part C. 1 point: The student shows a limited understanding of the volume of spheres and cylinders. The student answers only one part of the task correctly. 0 points: The student shows inconsistent or no understanding of the volume of spheres and cylinders. Version 1.0

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